Iterated differential forms III: Integral calculus

@article{Vinogradov2006IteratedDF,
  title={Iterated differential forms III: Integral calculus},
  author={Alexandre M. Vinogradov and Luca Vitagliano},
  journal={Doklady Mathematics},
  year={2006},
  volume={75},
  pages={177-180}
}
Basic elements of integral calculus over algebras of iterated differential forms �k, k < ∞, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra �∞ will be discussed in subsequent notes. 

Iterated differential forms: The Λk − 1-spectral sequence on infinite jets

In the preceding note math.DG/0610917 the $\Lambda_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic

Logic of differential calculus and the zoo of geometric strujctures

Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed that partial

References

SHOWING 1-10 OF 21 REFERENCES

Iterated differential forms: Tensors

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor

Iterated differential forms: Riemannian geometry revisited

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general

Geometry of nonlinear differential equations

The paper contains a survey of certain contemporary concepts and results connected with the geometric foundations of the theory of nonlinear partial differential equations. At the base of the account

Smooth Manifolds and Observables

Preface to English Edition.- Foreword.- Introduction.- Cutoff and other special smooth functions on R^n.- Algebras and points.- Smooth manifolds (algebraic definition).- Charts and atlases.- Smooth

Introduction to the Theory of Supermanifolds

CONTENTSIntroduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace §

Introduction to Superanalysis

1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir

Surveys

Soviet Math

  • Dokl. 13
  • 1972